Three women, Marion, Tina and Cathy went on a shopping spree. 90% of Marion's spending was equal to ¹₂ of Tina's spending. Cathy's spending was  40% more than Tina's. If Tina spent another $2106, she would spend the same amount of money as Cathy.

1. Find the ratio of Marion's spending to Tina's to Cathy's.
2. How much did Marion spend?

Marion	Tina	Cathy
5x5	9x5
	5x9	7x9
25 u	45 u	63 u

(a)
90%= ⁹⁰₁₀₀ = ⁹₁₀
⁹₁₀ of Marion's spending is equal to ¹₂ of Tina's spending. Make the numerators the same.  LCM of 9 and 1 is 9.

910 of Marion's spending = 12 of Tina's spending
910 of Marion's spending =1x92x9 of Tina's spending
910 of Marion's spending = 918 of Tina's spending

Marion : Tina
10 : 18
5 : 9

Cathy's spending in percent when compared to Tina's
= 100% + 40%
= 140%

Tina : Cathy
100 : 140
5 : 7

Tina's spending is the repeated identity.  Make Tina's spending the same.  LCM of 9 and 5 is 45.

Marion : Tina : Cathy
25 : 45 : 63

(b)

	Marion	Tina	Cathy
Before	25 u	45 u	63 u
Change		+ 18 u
After	25 u	63 u	63 u

Additional amount that Tina would have to spend to be the same as Cathy
= 63 u - 45 u
= 18 u

18 u = 2106

1 u = 2106 ÷ 18 = 117

Amount that Marion spent
= 25 u
= 25 x 117
= $2925 

Answer(s): (a) 25 : 45 : 63; (b) $2925